Statistical Mechanical Study of Molecular Fluids: Perturbation Theory and Computer Simulation

The first part of our work is based on thermodynamic perturbation theory in which the directional electrostatic forces between molecules contributing to the thermodynamic properties are evaluated through a series expansion about a reference potential model. We use the perturbation scheme introduced by Gubbins and Twu to study thermodynamic behavior of non-ideal fluids and their mixtures. This theory was shown to work very well for small molecules with strong polar and quadpolar forces (2,3). Henderson (4) in his review of equations of state and perterbation theories, describes the inaccuracy of the Carnahan Starling-type expressions for mixture of hard spheres when one of the components in the mixture is very large. Our first concern was to incorporate the intermolecular shape forces which are stronger and shorter ranged in the reference model, and apply a perterbation theory to account for the weaker and longer ranged electro-static forces. The rotational equation of state REOS (5) incorporates a new structural parameter alpha into the compressibility equation through inclusion of rotational motions of molecules in the partition function. In addition, the equation has been correlated to provide quantitative prediction of thermodynamic properties of pure normal paraffins up to n-C_ {20} (5). Using the three parameter REOS model as the reference together with the perturbation scheme of Gubbins and Twu, thermodynamic behavior of some non -ideal mixtures were studied. In this work, we use the 4-parameter BACK (7) as reference equation in the Gubbins -Twu perturbation scheme to predict volumetric behavior of pure polar compounds. The energy parameter epsilon_{x} and size parameter sigma_{x} of the mixture was calculated from the van-der-Waals 1 mixing rules (10). A new mixing rule for alpha _{x} is proposed which is established through an optimization process for all non-polar mixtures studied here. The second part of this work involves molecular simulation studies of fluids using the grand canonical ensemble Monte Carlo simulation (GCEMC) method. It is one of the best methods for study of fluid behavior in the phase boundary and critical regions where the canonical ensemble of finite size is inappropriate because of the suppression of concentration and density fluctuations. The emphasis in this work was the development of an improved algorithm for the implementation of the GCEMC method. The new algorithm can reduce the size of fluctuation to 20% of those in the original Adams' algorithm (11). The main characteristic of the new algorithm is the use of a sequence of ensembles with different number of molecules and this equilibrium in the regular canonical way. Then the decision for moving from one canonical ensemble to another with different number of molecules is based on the average energies calculated within the simulation. This algorithm is also better for the study of high density liquids, where the standard method fails due to the very small probability of acceptance of any addition of molecule. (Abstract shortened by UMI.).